Index of sphericity

The Index of Sphericity (${\displaystyle I_{s}}$) is a novel mathematical method described by Paul Gagniuc in 2015, that allows the quantification of various 2D irregular shapes. Let us consider that an unknown object intersects a two-dimensional plane. By studying the shape left by the unknown object on the two-dimensional plane, we can determine how spherical the unknown object is.

The values used for finding the Index of Sphericity are the perimeter and the area of an irregular shape measured on a two-dimensional plane. The Index of Sphericity (${\displaystyle I_{s}}$) considers two parameters: 1) the shape perimeter (${\displaystyle P_{m}}$) measured on a 2D surface and 2) a relative parameter, namely the mean shape diameter (${\displaystyle d_{m}}$). The mean shape diameter (${\displaystyle d_{m}}$) is determined from the perimeter and the area of the irregular shape. Thus, the shape diameter can be calculated using the perimeter (${\displaystyle d_{ip}}$) or the area (${\displaystyle d_{ia}}$):

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